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3 years ago

What is the greatest common factor of 15x^3y^2 and 20x^4y^4?

Mathematics

1 answer:

Vanyuwa [196]3 years ago

6 0

<h3>What is the greatest common factor of 15x³y² and 20x⁴y⁴? </h3>

First we have to find the factors of 15x³y²

15x³y² = 3 * 5x³y²

Then we have to find the factors of 20x⁴y⁴

20x⁴y⁴ = 2²x¹y² * 5x³y²

Now we have to find the common factors to both numbers.

The common factors are 5x³y²

Answer : GCF = (15x³y²,20x⁴y⁴) = 5x³y²

Hope this helps!

$\textit{\textbf{Spymore}}$

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Option D: Two irrational solutions

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The equation is $17+3 x^{2}=6 x$

Subtracting 6x from both sides, we have,

$3x^{2} -6x+17=0$

Solving the equation using quadratic formula,

$x=\frac{6 \pm \sqrt{36-4(3)(17)}}{2(3)}$

Simplifying the expression, we get,

$\begin{aligned}x &=\frac{6 \pm \sqrt{36-204}}{6} \\&=\frac{6 \pm \sqrt{-168}}{6} \\&=\frac{6 \pm 2 i \sqrt{42}}{6}\end{aligned}$

Taking out the common terms and simplifying, we have,

$\begin{aligned}x &=\frac{2(3 \pm i \sqrt{42})}{6} \\&=\frac{(3 \pm i \sqrt{42})}{3}\end{aligned}$

Dividing by 3, we get,

$x=1+i \sqrt{\frac{14}{3}}, x=1-i \sqrt{\frac{14}{3}}$

Hence, the equation has two irrational solutions.

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